Abstract:
We study the class of standardly stratified alge-
bras introduced by Cline, Parshall and Scott, and its subclass of the
so-called weakly properly stratified algebras, which generalizes the
class of properly stratified algebras introduced by Dlab. We char-
acterize when the Ringel dual of a standardly stratified algebra is
weakly properly stratified and show the existence of a two-step tilt-
ing module. This allows us to calculate the finitistic dimension of
such algebras. Finally, we also give a construction showing that
each finite partially pre-ordered set gives rise to a weakly properly
stratified algebras with a simple preserving duality.
